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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.geometry.euclidean.threed;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.geometry.Vector;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.geometry.euclidean.oned.Euclidean1D;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.geometry.euclidean.oned.IntervalsSet;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.geometry.euclidean.oned.Vector1D;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.geometry.partitioning.Embedding;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.util.Precision;<a name="line.27"></a>
<FONT color="green">028</FONT>    <a name="line.28"></a>
<FONT color="green">029</FONT>    /** The class represent lines in a three dimensional space.<a name="line.29"></a>
<FONT color="green">030</FONT>    <a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;Each oriented line is intrinsically associated with an abscissa<a name="line.31"></a>
<FONT color="green">032</FONT>     * which is a coordinate on the line. The point at abscissa 0 is the<a name="line.32"></a>
<FONT color="green">033</FONT>     * orthogonal projection of the origin on the line, another equivalent<a name="line.33"></a>
<FONT color="green">034</FONT>     * way to express this is to say that it is the point of the line<a name="line.34"></a>
<FONT color="green">035</FONT>     * which is closest to the origin. Abscissa increases in the line<a name="line.35"></a>
<FONT color="green">036</FONT>     * direction.&lt;/p&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>    <a name="line.37"></a>
<FONT color="green">038</FONT>     * @version $Id: Line.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.38"></a>
<FONT color="green">039</FONT>     * @since 3.0<a name="line.39"></a>
<FONT color="green">040</FONT>     */<a name="line.40"></a>
<FONT color="green">041</FONT>    public class Line implements Embedding&lt;Euclidean3D, Euclidean1D&gt; {<a name="line.41"></a>
<FONT color="green">042</FONT>    <a name="line.42"></a>
<FONT color="green">043</FONT>        /** Line direction. */<a name="line.43"></a>
<FONT color="green">044</FONT>        private Vector3D direction;<a name="line.44"></a>
<FONT color="green">045</FONT>    <a name="line.45"></a>
<FONT color="green">046</FONT>        /** Line point closest to the origin. */<a name="line.46"></a>
<FONT color="green">047</FONT>        private Vector3D zero;<a name="line.47"></a>
<FONT color="green">048</FONT>    <a name="line.48"></a>
<FONT color="green">049</FONT>        /** Build a line from two points.<a name="line.49"></a>
<FONT color="green">050</FONT>         * @param p1 first point belonging to the line (this can be any point)<a name="line.50"></a>
<FONT color="green">051</FONT>         * @param p2 second point belonging to the line (this can be any point, different from p1)<a name="line.51"></a>
<FONT color="green">052</FONT>         * @exception MathIllegalArgumentException if the points are equal<a name="line.52"></a>
<FONT color="green">053</FONT>         */<a name="line.53"></a>
<FONT color="green">054</FONT>        public Line(final Vector3D p1, final Vector3D p2) throws MathIllegalArgumentException {<a name="line.54"></a>
<FONT color="green">055</FONT>            reset(p1, p2);<a name="line.55"></a>
<FONT color="green">056</FONT>        }<a name="line.56"></a>
<FONT color="green">057</FONT>    <a name="line.57"></a>
<FONT color="green">058</FONT>        /** Copy constructor.<a name="line.58"></a>
<FONT color="green">059</FONT>         * &lt;p&gt;The created instance is completely independent from the<a name="line.59"></a>
<FONT color="green">060</FONT>         * original instance, it is a deep copy.&lt;/p&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>         * @param line line to copy<a name="line.61"></a>
<FONT color="green">062</FONT>         */<a name="line.62"></a>
<FONT color="green">063</FONT>        public Line(final Line line) {<a name="line.63"></a>
<FONT color="green">064</FONT>            this.direction = line.direction;<a name="line.64"></a>
<FONT color="green">065</FONT>            this.zero      = line.zero;<a name="line.65"></a>
<FONT color="green">066</FONT>        }<a name="line.66"></a>
<FONT color="green">067</FONT>    <a name="line.67"></a>
<FONT color="green">068</FONT>        /** Reset the instance as if built from two points.<a name="line.68"></a>
<FONT color="green">069</FONT>         * @param p1 first point belonging to the line (this can be any point)<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param p2 second point belonging to the line (this can be any point, different from p1)<a name="line.70"></a>
<FONT color="green">071</FONT>         * @exception MathIllegalArgumentException if the points are equal<a name="line.71"></a>
<FONT color="green">072</FONT>         */<a name="line.72"></a>
<FONT color="green">073</FONT>        public void reset(final Vector3D p1, final Vector3D p2) throws MathIllegalArgumentException {<a name="line.73"></a>
<FONT color="green">074</FONT>            final Vector3D delta = p2.subtract(p1);<a name="line.74"></a>
<FONT color="green">075</FONT>            final double norm2 = delta.getNormSq();<a name="line.75"></a>
<FONT color="green">076</FONT>            if (norm2 == 0.0) {<a name="line.76"></a>
<FONT color="green">077</FONT>                throw new MathIllegalArgumentException(LocalizedFormats.ZERO_NORM);<a name="line.77"></a>
<FONT color="green">078</FONT>            }<a name="line.78"></a>
<FONT color="green">079</FONT>            this.direction = new Vector3D(1.0 / FastMath.sqrt(norm2), delta);<a name="line.79"></a>
<FONT color="green">080</FONT>            zero = new Vector3D(1.0, p1, -p1.dotProduct(delta) / norm2, delta);<a name="line.80"></a>
<FONT color="green">081</FONT>        }<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>        /** Get a line with reversed direction.<a name="line.83"></a>
<FONT color="green">084</FONT>         * @return a new instance, with reversed direction<a name="line.84"></a>
<FONT color="green">085</FONT>         */<a name="line.85"></a>
<FONT color="green">086</FONT>        public Line revert() {<a name="line.86"></a>
<FONT color="green">087</FONT>            return new Line(zero, zero.subtract(direction));<a name="line.87"></a>
<FONT color="green">088</FONT>        }<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>        /** Get the normalized direction vector.<a name="line.90"></a>
<FONT color="green">091</FONT>         * @return normalized direction vector<a name="line.91"></a>
<FONT color="green">092</FONT>         */<a name="line.92"></a>
<FONT color="green">093</FONT>        public Vector3D getDirection() {<a name="line.93"></a>
<FONT color="green">094</FONT>            return direction;<a name="line.94"></a>
<FONT color="green">095</FONT>        }<a name="line.95"></a>
<FONT color="green">096</FONT>    <a name="line.96"></a>
<FONT color="green">097</FONT>        /** Get the line point closest to the origin.<a name="line.97"></a>
<FONT color="green">098</FONT>         * @return line point closest to the origin<a name="line.98"></a>
<FONT color="green">099</FONT>         */<a name="line.99"></a>
<FONT color="green">100</FONT>        public Vector3D getOrigin() {<a name="line.100"></a>
<FONT color="green">101</FONT>            return zero;<a name="line.101"></a>
<FONT color="green">102</FONT>        }<a name="line.102"></a>
<FONT color="green">103</FONT>    <a name="line.103"></a>
<FONT color="green">104</FONT>        /** Get the abscissa of a point with respect to the line.<a name="line.104"></a>
<FONT color="green">105</FONT>         * &lt;p&gt;The abscissa is 0 if the projection of the point and the<a name="line.105"></a>
<FONT color="green">106</FONT>         * projection of the frame origin on the line are the same<a name="line.106"></a>
<FONT color="green">107</FONT>         * point.&lt;/p&gt;<a name="line.107"></a>
<FONT color="green">108</FONT>         * @param point point to check<a name="line.108"></a>
<FONT color="green">109</FONT>         * @return abscissa of the point<a name="line.109"></a>
<FONT color="green">110</FONT>         */<a name="line.110"></a>
<FONT color="green">111</FONT>        public double getAbscissa(final Vector3D point) {<a name="line.111"></a>
<FONT color="green">112</FONT>            return point.subtract(zero).dotProduct(direction);<a name="line.112"></a>
<FONT color="green">113</FONT>        }<a name="line.113"></a>
<FONT color="green">114</FONT>    <a name="line.114"></a>
<FONT color="green">115</FONT>        /** Get one point from the line.<a name="line.115"></a>
<FONT color="green">116</FONT>         * @param abscissa desired abscissa for the point<a name="line.116"></a>
<FONT color="green">117</FONT>         * @return one point belonging to the line, at specified abscissa<a name="line.117"></a>
<FONT color="green">118</FONT>         */<a name="line.118"></a>
<FONT color="green">119</FONT>        public Vector3D pointAt(final double abscissa) {<a name="line.119"></a>
<FONT color="green">120</FONT>            return new Vector3D(1.0, zero, abscissa, direction);<a name="line.120"></a>
<FONT color="green">121</FONT>        }<a name="line.121"></a>
<FONT color="green">122</FONT>    <a name="line.122"></a>
<FONT color="green">123</FONT>        /** {@inheritDoc}<a name="line.123"></a>
<FONT color="green">124</FONT>         * @see #getAbscissa(Vector3D)<a name="line.124"></a>
<FONT color="green">125</FONT>         */<a name="line.125"></a>
<FONT color="green">126</FONT>        public Vector1D toSubSpace(final Vector&lt;Euclidean3D&gt; point) {<a name="line.126"></a>
<FONT color="green">127</FONT>            return new Vector1D(getAbscissa((Vector3D) point));<a name="line.127"></a>
<FONT color="green">128</FONT>        }<a name="line.128"></a>
<FONT color="green">129</FONT>    <a name="line.129"></a>
<FONT color="green">130</FONT>        /** {@inheritDoc}<a name="line.130"></a>
<FONT color="green">131</FONT>         * @see #pointAt(double)<a name="line.131"></a>
<FONT color="green">132</FONT>         */<a name="line.132"></a>
<FONT color="green">133</FONT>        public Vector3D toSpace(final Vector&lt;Euclidean1D&gt; point) {<a name="line.133"></a>
<FONT color="green">134</FONT>            return pointAt(((Vector1D) point).getX());<a name="line.134"></a>
<FONT color="green">135</FONT>        }<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>        /** Check if the instance is similar to another line.<a name="line.137"></a>
<FONT color="green">138</FONT>         * &lt;p&gt;Lines are considered similar if they contain the same<a name="line.138"></a>
<FONT color="green">139</FONT>         * points. This does not mean they are equal since they can have<a name="line.139"></a>
<FONT color="green">140</FONT>         * opposite directions.&lt;/p&gt;<a name="line.140"></a>
<FONT color="green">141</FONT>         * @param line line to which instance should be compared<a name="line.141"></a>
<FONT color="green">142</FONT>         * @return true if the lines are similar<a name="line.142"></a>
<FONT color="green">143</FONT>         */<a name="line.143"></a>
<FONT color="green">144</FONT>        public boolean isSimilarTo(final Line line) {<a name="line.144"></a>
<FONT color="green">145</FONT>            final double angle = Vector3D.angle(direction, line.direction);<a name="line.145"></a>
<FONT color="green">146</FONT>            return ((angle &lt; 1.0e-10) || (angle &gt; (FastMath.PI - 1.0e-10))) &amp;&amp; contains(line.zero);<a name="line.146"></a>
<FONT color="green">147</FONT>        }<a name="line.147"></a>
<FONT color="green">148</FONT>    <a name="line.148"></a>
<FONT color="green">149</FONT>        /** Check if the instance contains a point.<a name="line.149"></a>
<FONT color="green">150</FONT>         * @param p point to check<a name="line.150"></a>
<FONT color="green">151</FONT>         * @return true if p belongs to the line<a name="line.151"></a>
<FONT color="green">152</FONT>         */<a name="line.152"></a>
<FONT color="green">153</FONT>        public boolean contains(final Vector3D p) {<a name="line.153"></a>
<FONT color="green">154</FONT>            return distance(p) &lt; 1.0e-10;<a name="line.154"></a>
<FONT color="green">155</FONT>        }<a name="line.155"></a>
<FONT color="green">156</FONT>    <a name="line.156"></a>
<FONT color="green">157</FONT>        /** Compute the distance between the instance and a point.<a name="line.157"></a>
<FONT color="green">158</FONT>         * @param p to check<a name="line.158"></a>
<FONT color="green">159</FONT>         * @return distance between the instance and the point<a name="line.159"></a>
<FONT color="green">160</FONT>         */<a name="line.160"></a>
<FONT color="green">161</FONT>        public double distance(final Vector3D p) {<a name="line.161"></a>
<FONT color="green">162</FONT>            final Vector3D d = p.subtract(zero);<a name="line.162"></a>
<FONT color="green">163</FONT>            final Vector3D n = new Vector3D(1.0, d, -d.dotProduct(direction), direction);<a name="line.163"></a>
<FONT color="green">164</FONT>            return n.getNorm();<a name="line.164"></a>
<FONT color="green">165</FONT>        }<a name="line.165"></a>
<FONT color="green">166</FONT>    <a name="line.166"></a>
<FONT color="green">167</FONT>        /** Compute the shortest distance between the instance and another line.<a name="line.167"></a>
<FONT color="green">168</FONT>         * @param line line to check against the instance<a name="line.168"></a>
<FONT color="green">169</FONT>         * @return shortest distance between the instance and the line<a name="line.169"></a>
<FONT color="green">170</FONT>         */<a name="line.170"></a>
<FONT color="green">171</FONT>        public double distance(final Line line) {<a name="line.171"></a>
<FONT color="green">172</FONT>    <a name="line.172"></a>
<FONT color="green">173</FONT>            final Vector3D normal = Vector3D.crossProduct(direction, line.direction);<a name="line.173"></a>
<FONT color="green">174</FONT>            final double n = normal.getNorm();<a name="line.174"></a>
<FONT color="green">175</FONT>            if (n &lt; Precision.SAFE_MIN) {<a name="line.175"></a>
<FONT color="green">176</FONT>                // lines are parallel<a name="line.176"></a>
<FONT color="green">177</FONT>                return distance(line.zero);<a name="line.177"></a>
<FONT color="green">178</FONT>            }<a name="line.178"></a>
<FONT color="green">179</FONT>    <a name="line.179"></a>
<FONT color="green">180</FONT>            // signed separation of the two parallel planes that contains the lines<a name="line.180"></a>
<FONT color="green">181</FONT>            final double offset = line.zero.subtract(zero).dotProduct(normal) / n;<a name="line.181"></a>
<FONT color="green">182</FONT>    <a name="line.182"></a>
<FONT color="green">183</FONT>            return FastMath.abs(offset);<a name="line.183"></a>
<FONT color="green">184</FONT>    <a name="line.184"></a>
<FONT color="green">185</FONT>        }<a name="line.185"></a>
<FONT color="green">186</FONT>    <a name="line.186"></a>
<FONT color="green">187</FONT>        /** Compute the point of the instance closest to another line.<a name="line.187"></a>
<FONT color="green">188</FONT>         * @param line line to check against the instance<a name="line.188"></a>
<FONT color="green">189</FONT>         * @return point of the instance closest to another line<a name="line.189"></a>
<FONT color="green">190</FONT>         */<a name="line.190"></a>
<FONT color="green">191</FONT>        public Vector3D closestPoint(final Line line) {<a name="line.191"></a>
<FONT color="green">192</FONT>    <a name="line.192"></a>
<FONT color="green">193</FONT>            final double cos = direction.dotProduct(line.direction);<a name="line.193"></a>
<FONT color="green">194</FONT>            final double n = 1 - cos * cos;<a name="line.194"></a>
<FONT color="green">195</FONT>            if (n &lt; Precision.EPSILON) {<a name="line.195"></a>
<FONT color="green">196</FONT>                // the lines are parallel<a name="line.196"></a>
<FONT color="green">197</FONT>                return zero;<a name="line.197"></a>
<FONT color="green">198</FONT>            }<a name="line.198"></a>
<FONT color="green">199</FONT>    <a name="line.199"></a>
<FONT color="green">200</FONT>            final Vector3D delta0 = line.zero.subtract(zero);<a name="line.200"></a>
<FONT color="green">201</FONT>            final double a        = delta0.dotProduct(direction);<a name="line.201"></a>
<FONT color="green">202</FONT>            final double b        = delta0.dotProduct(line.direction);<a name="line.202"></a>
<FONT color="green">203</FONT>    <a name="line.203"></a>
<FONT color="green">204</FONT>            return new Vector3D(1, zero, (a - b * cos) / n, direction);<a name="line.204"></a>
<FONT color="green">205</FONT>    <a name="line.205"></a>
<FONT color="green">206</FONT>        }<a name="line.206"></a>
<FONT color="green">207</FONT>    <a name="line.207"></a>
<FONT color="green">208</FONT>        /** Get the intersection point of the instance and another line.<a name="line.208"></a>
<FONT color="green">209</FONT>         * @param line other line<a name="line.209"></a>
<FONT color="green">210</FONT>         * @return intersection point of the instance and the other line<a name="line.210"></a>
<FONT color="green">211</FONT>         * or null if there are no intersection points<a name="line.211"></a>
<FONT color="green">212</FONT>         */<a name="line.212"></a>
<FONT color="green">213</FONT>        public Vector3D intersection(final Line line) {<a name="line.213"></a>
<FONT color="green">214</FONT>            final Vector3D closest = closestPoint(line);<a name="line.214"></a>
<FONT color="green">215</FONT>            return line.contains(closest) ? closest : null;<a name="line.215"></a>
<FONT color="green">216</FONT>        }<a name="line.216"></a>
<FONT color="green">217</FONT>    <a name="line.217"></a>
<FONT color="green">218</FONT>        /** Build a sub-line covering the whole line.<a name="line.218"></a>
<FONT color="green">219</FONT>         * @return a sub-line covering the whole line<a name="line.219"></a>
<FONT color="green">220</FONT>         */<a name="line.220"></a>
<FONT color="green">221</FONT>        public SubLine wholeLine() {<a name="line.221"></a>
<FONT color="green">222</FONT>            return new SubLine(this, new IntervalsSet());<a name="line.222"></a>
<FONT color="green">223</FONT>        }<a name="line.223"></a>
<FONT color="green">224</FONT>    <a name="line.224"></a>
<FONT color="green">225</FONT>    }<a name="line.225"></a>




























































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